Search for Continuous Gravitational Waves from Spinning Neutron - - PowerPoint PPT Presentation

Search for Continuous Gravitational Waves from Spinning Neutron Stars

Speaker : Ling Sun Supervisor : Andrew Melatos OzGrav, University of Melbourne

Composite optical/X-ray image of the Crab Nebula (Optical: NASA/HST/ASU/J. Hester et al. X-Ray: NASA/CXC/ASU/J. Hester et al.)

Agenda

• Background (GW, detections, sources)
• Hidden Markov models
• Low-mass X-ray binary (LMXB) — Scorpius X-1
• Young supernova remnant (SNR) — SN1987A
• Post-merger remnant — GW170817
• Other contribution & future work

100 years ago… 1915 - 1916 Einstein predicted gravitational waves…

Source: Wikipedia

100 years later… 2015.09.14 LIGO detected the first gravitational-waves event!

More detections… … To be continued

Source: Wikimedia

What are gravitational waves?

Credit: Qimono/Flickr Credit: NASA/Dana Berry, Sky Works Digital

They are ‘ripples’ in the fabric of spacetime, traveling at the speed of light.

“Matter tells spacetime how to curve, and spacetime tells matter how to move.” — John Archibald Wheeler

What is Laser Interferometer Gravitational-Wave Observatory?

Credit: LIGO/Virgo

h0 = ∆L L

L = 4 km

∆L ∼ 10−19 m

1/10,000 of a proton!

Credit: The SXS (Simulating eXtreme Spacetimes) Project

Binary black hole coalescences

Credit: LIGO

LIGO/Virgo/NASA/Leo Singer (Milky Way image: Axel Mellinger)

GW150914 GW151226 LVT151012 GW170104 GW170814 GW170817 GW170608

Binary neutron star coalescence - GW170817

Credit: NASA GSFC & LIGO-Virgo

• Astrophys. J. Lett. 848, L12 (2017)

What else?

The Crab Nebula is a pulsar wind nebula associated with the 1054 supernova NASA, ESA, J. Hester and A. Loll (Arizona State University) Credit: ESA and the Planck Collaboration

Small h0 … Need longer observation and more computing cost

• Targeted searches for pulsars with known sky position and

ephemerides

• Directed searches for neutron stars with known sky position

but unknown rotation frequency

• All-sky searches over the entire sky for unknown neutron stars

Continuous wave data analysis categories

We do not know the spin frequency of the star

• Need to search a broad range of frequencies — a lot computing cost

The spin frequency is wandering

• Internal - fluctuating magnetospheric or superfluid torques
• External - fluctuating accretion torque
• Can not do coherent search over a long duration

Challenges in directed searches Rapid spin down of young targets

• Need to search higher time derivatives of frequency

Hidden Markov models

[1] Suvorova, Sun, Melatos, Moran, Evans, Phys. Rev. D 93, 123009 (2016)

Hidden Markov Model

• Markov Chain - A random process with discrete states, changing from
• ne state to another; The next state only depends on the current state;

The transition is governed by a transition probability matrix.

• Hidden Markov Model - States are not directly observable.

LIGO noisy raw data Spin-wandering GW signal

Viterbi Algorithm and Optimal Path

Tracking Spin-wandering Signals

h0 = 3 x 10-25

h0 = 1 x 10-25 h0 = 6 x 10-26

h0 = 6 x 10-26

h0 = 2 x 10-26

Signal from isolated NS under aLIGO design sensitivity

Low-mass X-ray binaries (LMXBs) — HMM tracking

[2] LIGO Scientific Collaboration and Virgo Collaboration, Phys. Rev. D 95, 122003 (2017)

Image: An artist's impression of the Scorpius X-1 LMXB system Credit: Ralf Schoofs

Low-mass X-ray binary (LMXB)

Image: Tauris et al., Formation and evolution of compact stellar X-ray sources

• Torque-balance theory —

accretion spins the star up; GW emission slows it down

Image: Sammut PhD Thesis (2015)

Why is Scorpius X-1 interesting?

• Accretion in LMXB is a natural method of powering GW emission.

Image: Tauris et al., Formation and evolution of compact stellar X-ray sources

• Torque-balance theory — accretion spins the star up; GW

emission slows it down — the more X-ray luminous, the stronger GW emission

• Scorpius X-1 — the brightest LMXB in our galaxy; sky position

and orbital period well observed

h+,×(t) ∝

∞

X

n=−∞

Jn(2πf0a0) cos[2π(f0 + n/P)t]

Before HMM tracking…

Intermediate polar animation by Dr Andy Beardmore, Keele University

• Signal is Doppler modulated

a0 - projected semi-major axis P - orbital period

Use a Bessel-weighted matched filter

Remove the Doppler modulation

A true signal with that strain amplitude would produce a signal power stronger than what was measured in the data 95% (or more) of the time.

Search results in the first Advanced LIGO observing run

Abbott et al., Phys. Rev. D. 95, 122003 (2017)

Image: An artist's impression of the Scorpius X-1 LMXB system Credit: Ralf Schoofs

Low-mass X-ray binaries (LMXBs) — Sideband search

[3] Sun, Melatos, Sammut, LIGO-T1600457 (2016)

Sideband Search (Advanced LIGO O1)

Sammut et al., PRD 89, 043001 (2014)

• Only search a 10-day data stretch (avoid the impact of spin wandering)
• The search was conducted using the Initial LIGO S5 data
• Less sensitive than HMM tracking
• O1 results improve on previously published S5 results by a factor of ~4

Young supernova remnants (SNRs) — Cross-correlation search

[4] Sun, Melatos, Lasky, Chung, Darman, Phys. Rev. D 94, 082004 (2016)

• A semi-coherent search strategy

(Dhurandhar et al. 2008; Chung et al. 2011)

• Short Fourier Transform (SFT) segments

(30 min) for long Tobs (1 year, 4 months, etc.)

Cross-Correlation Method

} Tlag = 1 hr } Tlag = 1 hr

Credit: J. T. Whelan

2 hrs

Detection Statistic

Weights - parameters of the source, including

1) Fast phase evolution terms (i.e. f, f’, etc.) 2) Slow functions of orientation (i.e. ψ, ι, etc.)

• Detection statistic is a weighted sum of over all SFT pairs.
• SFTs are paired and multiplied

Search over

Phase Tracking for Young Target

{ν, ˙ ν, ¨ ν, ... ν , · · · } {ν0, Q1, Q2, n} instead of

Q1 ∝ ✏2 Q2 ∝ B2

Gravitational spin down Electromagnetic spin down

• Type II core-collapse supernova

(February 1987)

• Large Magellanic Cloud (α = 5h 35m

28.03s, δ = −69◦16′11.79′′, d = 51.4 kpc.)

• Initial LIGO upper limit h0 ~ 3.8 x 10-25

Cross-Correlation Search for SN 1987A (Initial LIGO S5)

Sun et al., 2016

Young supernova remnants (SNRs) — HMM tracking

[5] Sun, Melatos, Suvorova, Moran, Evans, arXiv:1710.00460 (2017)

Frequency tracking

• Allow to move at most
• ne bin over each step
• Short step size is required
• Emission probabilities: 1-D

maximum likelihood estimator Weak spin wandering (timing noise)

Tracking Example

| ˙ f0| ∼ 10−11 Hzs−1

Frequency tracking

Strong spin wandering (timing noise)

Tracking Example

| ˙ f0| ∼ 10−11 Hzs−1

| ˙ f0| ∼ 10−8 Hzs−1

Rapid spin down, negligible spin wandering

An alternative: 2-D tracking

• Allow to move at most one bin over each step
• Track limited frequency range according to
• Emission probabilities: 2-D maximum likelihood estimator

2-D Tracking Example

| ˙ f0| ∼ 10−8 Hzs−1

GW170817 post-merger remnant — HMM tracking

[5] Sun, Melatos, Suvorova, Moran, Evans, arXiv:1710.00460 (2017)

Image: Artist’s illustration of two merging neutron stars. (Credit: NSF/ LIGO/Sonoma State University/ Aurore Simonnet)

• Prompt formation of a BH
• Hypermassive NS that collapses to a BH in ~ < 1s
• Supramassive NS that collapses to a BH on timescales of ~10 − 104 s
• Formation of a stable NS

What is left over after GW170817?

Credit: T. Dietrich, S. Ossokine, H. Pfeiffer, A. Buonanno/Max Planck Institute for Gravitational Physics/BAM collaboration

• HMM tracking can be

readily applied to the post-merger search for long-duration quasi-CW signals (spin-down timescale ~102 —104 s)

• Unmodelled search;

allow the spinning-down signal to wander

• Use 1-sec SFTs to cope

with the extremely rapid spin down

Tracking Samples

What is left over after GW170817?

Other contribution

• Advanced LIGO O1 Hardware

injection verification

• Test the front-end calibration
• HMM tracking for Sco X-1 v2.0

(led by Clearwater & Suvorova)

[6] Biwer et al, Phys. Rev. D 95, 062002 (2017) [7] Suvorova, Clearwater, Melatos, Sun, Moran, Evans, Hidden, arXiv:1710.07092, accepted for publication in PRD (2017)

Credit: Joe McNally/Getty Images

Ongoing & Future work

• Complete the GW170817 post-merger remnant search
• Further improve the methods, and search upcoming interferometer data
• Search other CW sources, e.g., ultralight boson cloud around a BH
• Extend my research to gravitational-wave physics more broadly

Thanks! Questions?